CN107239821A - Group of cities transportation network reliability restorative procedure under random attack strategies - Google Patents
Group of cities transportation network reliability restorative procedure under random attack strategies Download PDFInfo
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Abstract
The present invention relates to transportation network field, the group of cities transportation network reliability restorative procedure under especially random attack strategies, its method and step is：Step 1 is structure group of cities traffic network design；Step 2 emulates for group of cities transportation network cascading failure；Step 3 is based on the group of cities transportation network reliability restorative procedure for improving binary particle swarm algorithm.The present invention considers load with the characteristic for repairing node state change, and the process that pause node load can be shared to normal node in network is analyzed, and can more objectively describe group of cities traffic flow phenomenon.Propose fine disturbing operator, speed Chaos Search operator, the fine degree that on the one hand increase understands, the ability of searching optimum that on the other hand increase understands；And Restricted operator is repaired so that all particles are feasible solutions to ensure efficient, the simplicity of algorithm, and be used in during group of cities transportation network repairs, farthest recover the reliability of group of cities transportation network.
Description
Technical field
The present invention relates to transportation network field, the group of cities transportation network reliability under especially random attack strategies is repaired
Method.
Background technology
With continuing to develop for group of cities, the various transportation networks in group of cities are increasingly complicated, transportation network reliability
Facing challenges are on the increase.Website in group of cities transportation network, once in face of major natural disasters, the load of node occurs
Change so that passenger-cargo other websites that flow in website flow, and then cause the load of remaining website is excessive to cause website to fail,
Vicious circle is formed with this.Cause conevying efficiency significantly to decline, drastically influence the normal production and living safety of the people.Cause
How this, quickly and efficiently repaired to network using limited resource, recover network function in time, be that this method is focused on
The problem of solution.This method can look for after random anomalous event occurs preferably correcting strategy, at utmost to recover network
Reliability.In addition, this method has stronger practical value, it is possible to reduce influence group of cities normal because part website fails
The brought economic loss of operating, improves the ability that network resists anomalous event influence.
In recent years, reliability consideration of the scholars to transportation network is more and more.Wang Yunqin in master thesis, with
The relative size of two measures index, network efficiency and maximal connected subgraphs have studied the reliability of Beijing Rail Transit network.
Kind of roc cloud etc. using cascading failure average size as Survivabilities of Networks evaluation measure index, to hazardous materials transportation related network
Cascading failure mechanism is emulated.Zhao Miao is uncommon to be waited based on the point power in network, it is proposed that Rail traffic network measurement index
Method.With deepening continuously for transportation network reliability consideration, Cheng Jie et al. is based on cascading failure principle, it is proposed that a kind of city
The restorative procedure of transportation network, and contrasted with common complex network correcting strategy.Positive force of king et al. is based in network
The repairing effect of node, the importance ranking according to node proposes a kind of restorative procedure of urban highway traffic.
Current Urban Agglomeration Development is rapid, and there has been no correlative study for the restorative procedure of group of cities transportation network.
In terms of urban traffic network reparation, its efficiency of algorithm of the restorative procedure of Cheng Jie et al. propositions is relatively low.And city group node is numerous, section
Company frontier juncture between point is intricate, and this method will be difficult to be applied among group of cities transportation network.Positive force of king et al. proposes
Restorative procedure, do not account for the weight on side, that is, the weight for thinking all sides is the same.And in group of cities transportation network
In, passenger-cargo stream that part circuit undertakes is larger, then the weight of corresponding edge is just higher.In addition, above method thinks that load exceedes
Its capacity, then the node just fail.But, in actual transportation network, node has certain redundant ability toward contact.
The operational efficiency of node is low at this moment, and the state of node is to correspond to halted state, but at present on transportation network reparation
Research do not account for the situation.And cause pause node to recover normal feelings without one node of reparation is studied
Condition.
Therefore, it is necessary to propose the group of cities transportation network reliability reparation side under random attack strategies for above mentioned problem
Method.
The content of the invention
For above-mentioned the deficiencies in the prior art, it is an object of the invention to provide the city under random attack strategies
Flock-mate open network reliability restorative procedure, reliability is recovered as target to maximize, and is that the reparation of transportation network proposes science, height
The scheme of effect.
Group of cities transportation network reliability restorative procedure under random attack strategies, it is characterised in that：Its method and step is：
Step 1 is structure group of cities traffic network design；Step 2 emulates for group of cities transportation network cascading failure；Step 3 is based on changing
Enter the group of cities transportation network reliability restorative procedure of binary particle swarm algorithm, the step 1 also includes：
Step 1.1：The classification existed according to group of cities transportation network, builds in single traffic network design, such as group of cities
In the presence of four kinds of means of transportation, then need to build Traffic Net model, Rail traffic network model, air transportation network mould respectively
Type, water-borne transport network model；
Step 1.2：In various traffic network designs, if bus station, railway station, airport, harbour geographical position it is nearer,
Then node is overlapped, a node is regarded it as in group of cities transportation network；
Step 1.3：With the departure frequency of automobile, train start train number, the flight frequency of aircraft, ship course line class
The secondary weight respectively as side in Traffic Net, Rail traffic network, air transportation network, water-borne transport network.With
Entropy assessment tries to achieve the significance level of every kind of means of transportation, and finally side ij weight ew (i, j) attaches most importance in group of cities transportation network
Want degree and the product of side right weight in single transportation network；
Step 1.4：Gather number according to bus station, railway station, airport, passenger's highest at harbour, determine nodes i
Capacity c (i).Node capacity after being then superimposed is superposition front nodal point capacity sum.
Step 1.1 further comprises：Step 1.1.1：Using the bus station in group of cities as the node in Traffic Net,
There is a line if between bus station being open to traffic, between node to be connected, Traffic Net model is built with this；
Step 1.1.2：Using the railway station in group of cities as the node in Rail traffic network, if there is track between railway station
Circuit is connected, then there is a line between node and be connected, Rail traffic network model is built with this；
Step 1.1.3：Node in using the airport in group of cities as air transportation network, if there is flight to fly between airport
OK, then there is a line between node to be connected, air transportation network model is built with this；
Step 1.1.4：Node in using the harbour in group of cities as water-borne transport network, if there is navigation ship between harbour
, then there is a line between node and be connected, water-borne transport network model is built with this in oceangoing ship.
Step 2 further comprises：Step 2.1：According to capacity coefficient α, it may be determined that node i is not attacking the load l at moment
(i) such as formula (1)；
L (i)=α × c (i) (1)
Step 2.2：With the strategy attack node i attacked at random；
Step 2.3：Node i fails, and normal condition is judged whether and connected node j, if the load l (i) in the presence of if
Distribute to coupled node j, node j load such as formula (2).Step 2.5 is gone to if being not present；
Wherein, d (j) is node j node degree, i.e. the connected side number of node, and Φ is the collection of normal node of being connected with node i
Close.
Step 2.4：Judge connected node j state；
Wherein, β is overload factor.If node failure, step 2.3 is gone to, step 2.5 is otherwise gone to；
Step 2.5：Judge that pause node whether there is the normal connected node of state, divide if there is load is then carried out
Match somebody with somebody；
Step 2.6：Judge whether to travel through all pause nodes, if then judging all node states according to formula (3), and turn
To step 2.7, step 2.5 is otherwise gone to；
Step 2.7：Iterations is updated, and judges whether iterations is less than number of times of attack, such as iterations is less than and attacked
Number of times is hit, then return to step 2.2, otherwise terminate cascading failure emulation.
Step 3 further comprises：Step 3.1：If if there is dried particle in population, each particle is then a kind of recovery scenario,
The dimension all same of particle, i.e. failure node number n.Speed and position are initialized, and calculate the suitable of each particle
Response；
Step 3.2：To ranking fitness, advantage particle, ordinary particle and inferior position are selected from the population of initialization
Particle；
Step 3.3：The position of each particle corresponds to a speed, then the speed of j-th of dimension is v in particle iij, more
New speed such as formula (4)；
vij=w × vij+rand×c1×(pibij-pij)+rand×c2×(pgbj-pij) (4)
Wherein, w is inertia weight, and rand is 0 to 1 random number, c1,c2Respectively the self-teaching factor and social learning
The factor, pibijFor the value of i-th of particle adaptive optimal control j-th of dimension of degree, pgbjFor all particle history adaptive optimal control degree jth
The value of individual dimension；
Step 3.4：The speed of advantage particle is disturbed with fine disturbing operator；
Step 3.5：The speed of inferior position particle is updated with speed Chaos Search operator；
Step 3.6：More new formula such as formula (5) according to the speed, then particle i positions j of particle；
Step 3.7：Row constraint is entered to the position of each particle with Restricted operator is repaired；
Step 3.8：Each particle i fitness f (i) is calculated, if f (i) ＞ fib (i), by particle i position assignment
Position when particle i adaptive optimal controls are spent, more new particle i adaptive optimal control degree.If f (i) ＞ fgb, particle i position is assigned
It is worth position when history adaptive optimal control is spent in all particles, updates all particle history adaptive optimal control degree, position and speed.Its
In, fib (i) is the optimal fitness of particle i, and fgb is the optimal fitness of all particle history；
Step 3.9：To ranking fitness, advantage particle, ordinary particle and inferior position particle are selected from population；
Step 3.10：Iterations is updated, judges whether to have reached greatest iteration number, step 3.3 is turned to if not meeting,
History adaptive optimal control degree in population and its position are exported if meeting.The node that its position is corresponded to repair, the i.e. program
It is then group of cities transportation network preferably recovery scenario.
Three kinds of states of the invention according to node, it is contemplated that cascading failure phenomenon present in transportation network, can be imitative
Very, the influence between egress and node is embodied in repairing.According in network while importance for while impart weight, Neng Gouzhun
True measurement group of cities transportation network reliability is by being influenceed.Consider load with the characteristic for repairing node state change, i.e., it is every
The process of pause node load can be shared by repairing normal node in a failure node, network, can more objectively be described
Group of cities traffic flow phenomenon.Improve binary particle swarm algorithm, it is proposed that fine disturbing operator and speed Chaos Search are calculated
Son, is coordinated by advantage particle and inferior position particle cooperative and on the one hand improves the fine degree understood, on the other hand add particle
In the search capability of solution space.In addition repairing Restricted operator causes all particles to be feasible solution to ensure efficient, the letter of algorithm
Just, and it has been used in during group of cities transportation network repairs, using the teaching of the invention it is possible to provide preferably recovery scenario, has farthest recovered city
The reliability of city's flock-mate open network.
Brief description of the drawings
Fig. 1 is that group of cities transportation network builds schematic diagram；
Fig. 2 is group of cities transportation network cascading failure mechanism schematic diagram；
Fig. 3 is improvement binary particle swarm algorithm schematic diagram；
Fig. 4 is the load and state change schematic diagram of all nodes after node is repaired；
Fig. 5 is the weight schematic diagram on Hu Bao Echeng city's flock-mate open network side；
Fig. 6 is Hu Bao Echeng city's flock-mate open network adjacency matrix schematic diagram；
Fig. 7 is Hu Bao Echeng city's flock-mate open network by the lower reliability measure index change schematic diagram of random attack；
Fig. 8 be based on improve binary particle swarm algorithm under, the modified-image of population history adaptive optimal control degree.
Embodiment
Embodiments of the invention are described in detail below in conjunction with accompanying drawing, but the present invention can be defined by the claims
Implement with the multitude of different ways of covering.
Such as Fig. 1 and with reference to shown in Fig. 2 to Fig. 8, the group of cities transportation network reliability restorative procedure under random attack strategies,
It is characterized in that：Its method and step is：Step 1 is structure group of cities traffic network design；Step 2 is group of cities transportation network level
Join failure simulation；Step 3 is the group of cities transportation network reliability restorative procedure based on improvement binary particle swarm algorithm, described
Step 1 also includes：
Step 1.1：The classification existed according to group of cities transportation network, builds in single traffic network design, such as group of cities
In the presence of four kinds of means of transportation, then need to build Traffic Net model, Rail traffic network model, air transportation network mould respectively
Type, water-borne transport network model；
Step 1.2：In various traffic network designs, if bus station, railway station, airport, harbour geographical position it is nearer,
Then node is overlapped, a node is regarded it as in group of cities transportation network；
Step 1.3：With the departure frequency of automobile, train start train number, the flight frequency of aircraft, ship course line class
The secondary weight respectively as side in Traffic Net, Rail traffic network, air transportation network, water-borne transport network.With
Entropy assessment tries to achieve the significance level of every kind of means of transportation, and finally side ij weight ew (i, j) attaches most importance in group of cities transportation network
Want degree and the product of side right weight in single transportation network；
Step 1.4：Gather number according to bus station, railway station, airport, passenger's highest at harbour, determine nodes i
Capacity c (i).Node capacity after being then superimposed is superposition front nodal point capacity sum.
Step 1.1 further comprises：Step 1.1.1：Using the bus station in group of cities as the node in Traffic Net,
There is a line if between bus station being open to traffic, between node to be connected, Traffic Net model is built with this；
Step 1.1.2：Using the railway station in group of cities as the node in Rail traffic network, if there is track between railway station
Circuit is connected, then there is a line between node and be connected, Rail traffic network model is built with this；
Step 1.1.3：Node in using the airport in group of cities as air transportation network, if there is flight to fly between airport
OK, then there is a line between node to be connected, air transportation network model is built with this；
Step 1.1.4：Node in using the harbour in group of cities as water-borne transport network, if there is navigation ship between harbour
, then there is a line between node and be connected, water-borne transport network model is built with this in oceangoing ship.
Step 2 further comprises：Step 2.1：According to capacity coefficient α, it may be determined that node i is not attacking the load l at moment
(i) such as formula (1)；
L (i)=α × c (i) (1)
Step 2.2：With the strategy attack node i attacked at random；
Step 2.3：Node i fails, and normal condition is judged whether and connected node j, if the load l (i) in the presence of if
Distribute to coupled node j, node j load such as formula (2).Step 2.5 is gone to if being not present；
Wherein, d (j) is node j node degree, i.e. the connected side number of node, and Φ is the collection of normal node of being connected with node i
Close.
Step 2.4：Judge connected node j state；
Wherein, β is overload factor.If node failure, step 2.3 is gone to, step 2.5 is otherwise gone to；
Step 2.5：Judge that pause node whether there is the normal connected node of state, divide if there is load is then carried out
Match somebody with somebody；
Step 2.6：Judge whether to travel through all pause nodes, if then judging all node states according to formula (3), and turn
To step 2.7, step 2.5 is otherwise gone to；
Step 2.7：Iterations is updated, and judges whether iterations is less than number of times of attack, such as iterations is less than and attacked
Number of times is hit, then return to step 2.2, otherwise terminate cascading failure emulation.
Step 3 further comprises：Step 3.1：If if there is dried particle in population, each particle is then a kind of recovery scenario,
The dimension all same of particle, i.e. failure node number n.Speed and position are initialized, and calculate the suitable of each particle
Response；
Step 3.2：To ranking fitness, advantage particle, ordinary particle and inferior position particle are selected from population；
Step 3.3：The position of each particle corresponds to a speed, then the speed of j-th of dimension is v in particle iij, more
New speed such as formula (4)；
vij=w × vij+rand×c1×(pibij-pij)+rand×c2×(pgbj-pij) (4)
Wherein, w is inertia weight, and rand is 0 to 1 random number, c1,c2Respectively the self-teaching factor and social learning
The factor, pibijFor the value of i-th of particle adaptive optimal control j-th of dimension of degree, pgbjFor all particle history adaptive optimal control degree jth
The value of individual dimension；
Step 3.4：The speed of advantage particle is disturbed with fine disturbing operator；
Step 3.5：The speed of inferior position particle is updated with speed Chaos Search operator；
Step 3.6：More new formula such as formula (5) according to the speed, then particle i positions j of particle；
Step 3.7：Row constraint is entered to the position of each particle with Restricted operator is repaired；
Step 3.8：Each particle i fitness f (i) is calculated, if f (i) ＞ fib (i), by particle i position assignment
Position when particle i adaptive optimal controls are spent, more new particle i adaptive optimal control degree.If f (i) ＞ fgb, particle i position is assigned
It is worth position when all particle history adaptive optimal controls are spent, updates all particle history adaptive optimal control degree and speed.Wherein, fib
(i) it is fitness optimal particle i, fgb is the optimal fitness of all particle history；
Step 3.9：Particle in population is evaluated, advantage particle, ordinary particle and inferior position particle is selected；
Step 3.10：Iterations is updated, judges whether to have reached greatest iteration number, step 3.3 is turned to if not meeting,
History adaptive optimal control degree in population and its position are exported if meeting.The node that its position is corresponded to repair, the i.e. program
It is then group of cities transportation network preferably recovery scenario.
Case study on implementation one：
Inventive method is described in detail below in conjunction with Hu Bao Hubei Province group of cities example.
Step 1：In the group of cities of Hu Bao Hubei Province, bus station is numerous with railway station, road transport mode and rail transport mode
Undertake passenger-cargo large percentage.Therefore, Traffic Net model and Rail traffic network model are built, structure is superimposed to both and exhaled
Wrap Echeng city group's traffic network design.
Step 1.1：According to internet and the transport management bureau in Bao Esan cities is exhaled, to the bus station in the group of cities of Hu Bao Hubei Province, vapour
Fare road, departure frequency, website highest gather number and are obtained and counted.By bus station it is abstract be node, if two bus stations
Between with the presence of circuit be connected then corresponding node a line be connected, departure frequency is designated as to the weight on side in Traffic Net,
The highest of website is gathered into the capacity that number is designated as node, Traffic Net model is built with this.
Step 1.2：According to internet and the railway station in Bao Esan cities is exhaled, to the railway station in the group of cities of Hu Bao Hubei Province, fire
Fare road, the start train number, website highest of train gather number and are obtained and counted.By railway station it is abstract be node, if
It is connected between railway station with the presence of the connected then corresponding node a line of circuit, the train number of starting of train is designated as rail transit network
The weight on side in network, gathers the capacity that number is designated as node by the highest of website, Rail traffic network model is built with this.
Step 1.3：According to transport management bureau, the railway station for exhaling Bao Esan cities, investigation draws road transport mode, rail transport side
Passenger-cargo freight volume, the volume of the circular flow of formula.It can show that the significance level of road transport mode is 0.6627, rail transport side according to entropy assessment
The significance level of formula is 0.3373.Then in group of cities transportation network while weight for significance level and single transportation network in while
Weight product.Finally, the weight on group of cities transportation network side is as shown in Figure 5.
Step 1.4：Nearer node is overlapped, a node is regarded as in group of cities transportation network, to holding
Amount summation then draws the capacity of superposition posterior nodal point.If there are multiple summits between two nodes to be connected, the weight of opposite side is also needed to carry out
Summation, is regarded as a line and is connected, and Hu Bao Echeng city group's traffic network design is built with this.
Step 1.5：Its adjacency matrix AM, such as Fig. 6 can be drawn by Hu Bao Echeng city's flock-mate open network.If node i and node j
Between exist side be connected, then in adjacency matrix AM the i-th row jth row and jth row the i-th column of figure be 1, be otherwise 0.
Step 2：Hu Bao Hubei Province group of cities cascading failure Reliablility simulation, step 2.1：Capacity coefficient α=0.7 is made, according to formula
(1) it is the initial load that can determine that each node, 50 nodes of attack, iterations t=0, and the section in calculating network at random
Point degree.
Step 2.2：Node k is randomly choosed in the group of cities of Hu Bao Hubei Province to be attacked.
Step 2.3：Node k fails, then in adjacency matrix AM so that the numeral that row k is arranged with kth is 0.
Step 2.4：Find out the normal node being connected with failure node.If in the presence of basis (2) formula is divided load
Match somebody with somebody, otherwise go to step 2.6.
Step 2.5：Overload factor β=1.2 are made, according to (3) formula, the state to connected node judges, if node is
Failure state, then go to step 2.3, otherwise go to step 2.6.Step 2.6：Judge that pause node is normal with the presence or absence of state
Connected node, if there is then carrying out sharing of load, operating load assignment operators.
Sharing of load operator
Step (a)：Judge node h of the state for pause, if there is coupled and state for normal node s.If
It is not present, then goes to step (e).If in the presence of going to step (b).
Step (b)：Pause node h sub-loads are allocated in node s.Then sharing of load amount Δ l is calculated such as formula (8).
Δ l=min { l (h)-c (h), c (s)-l (s) } (8)
Wherein, min { l (h)-c (h), c (s)-l (s) } represents that selection is less from l (h)-c (h) and c (s)-l (s)
Value.
Step (c)：According to sharing of load amount Δ l, the load of more new node, such as formula (9), formula (10).
L (s)=l (s)+Δ l (9)
L (h)=l (h)-Δ l (10)
Step (d)：The state of all nodes is updated according to formula (3).
Step (e)：Judge whether traversal institute it is stateful for suspend node, if it is operator terminate；Otherwise step is gone to
Suddenly (a).
Step 2.7：Judge all node states according to formula (3).
Step 2.8：Calculate reliability measure index E.
Step 2.8.1：According to while while between weight, be the distance between arbitrary node o, q disoqAssignment such as formula
(6)。
Step 2.8.2：With folyd shortest path algorithms, calculating does well as the beeline between normal node o, q
dis′oq, reliability measure index E, calculation formula such as formula (7) are calculated with this.
Wherein, N is the number of nodes, and Ω is the set of nodes.
Step 2.9：T=t+1.Judge whether iterations t is less than number of times of attack.Such as iterations is less than number of times of attack,
Then return to step 2.2.Conversely, terminating cascading failure emulation, and the state of node, load, capacity are exported.After under fire
The state of node, the reliability of network are as shown in table 1, table 2, and the change of reliability measure index is as shown in Figure 7.
Step 3：Based on the group of cities transportation network reliability restorative procedure for improving binary particle swarm algorithm.
Step 3.1：There is n node failure in cascading failure simulation process, n=56 repairs nodes rn=30.Order kind
There are 100 particles in group, the dimension of each particle is 56, iterations 200 times, current iteration number of times t=0.The position of particle
Corresponding relation with node is as shown in table 3.
Step 3.2：Initialize speed and the position of particle.Because the speed of particle is excessive or too small is difficult to find that most
Excellent solution, therefore, the speed of all each dimensions of particle is in [vmin,vmax] in random value.V in the methodmin=-4, vmax
=4, and make hdjs=0.The position of particle then takes 0 or 1 at random.
Step 3.3：Calculate the fitness of initialization particle.
Step 3.3.1：Particle i position j is corresponded into failure node k, if particle i position j is 1, node k is repaiied
Multiple, its load l (k)=0, node state is normal, the row k in adjacency matrix AM where failure node, and kth row recover not
Value before failure.Such as position is 0, is not otherwise repaired.
Step 3.3.2：After after node reparation, because its state is normal, therefore one of the pause node that is connected can be undertaken
Divide load, in order to describe the phenomenon, operating load assignment operators.
Step 3.3.3：Calculate particle i fitness f (i), you can by property measurement index E.Due to pause node and failure
Node can not run well, therefore it is normal node, calculation formula such as formula (7) only to calculate state.
Step 3.4：Fitness is ranked up, y% particle is advantage particle before fitness in selection initialization particle,
It is inferior position particle to select the particle of y% fitness rearward, and remaining is then ordinary particle, and y takes 20 in the method.
Step 3.5：Particle i speed j is updated according to (4) formula, madec1=2,
c2=2.Wherein, wmax, wminW in the respectively maximum of inertia weight and the minimum value of inertia weight, this methodmax=1, wmin
=0.5.
Step 3.6：Advantage particle largely decides algorithm performance in population, and the location-dependent query of advantage particle
Its speed.From formula (4) it can be found that in iteration later stage advantage particle due to similar so as to lose for self and population
Study, and speed is less and less under the influence of inertia weight, cause advantage particle be difficult to carry out the solution of problem it is fine
Search for, therefore this method is scanned for using fine disturbing operator.
Fine disturbing operator
Step (1)：The speed vgb of speed and population history adaptive optimal control degree particle is tieed up according to advantage particle r b, can be with
Calculate its disturbance quantity rdrb, such as formula (11).
In the method, δ=0.1.
Step (2)：The speed of advantage particle, more new formula such as (12) are updated according to the disturbance quantity of speed.
vrb=vrb(1+rdrb) (12)
Step (3)：If the speed of advantage particle exceedes border, it is limited.
Step (4)：Judge whether update all dimensions of advantageous particle speed, if then operator terminates, otherwise return
Return step (1).
Step 3.7：Advantage particle is often positioned in locally optimal solution in population, and is then difficult to look for when carrying out fine search
To globally optimal solution.Therefore, this is accomplished by inferior position particle and carries out global search to solution space.Because chaos principle has very well
Ergodic, unduplicated solution space can be scanned for, improves the possibility that population flees from locally optimal solution, therefore profit
The speed of inferior position particle is updated with speed Chaos Search operator.
Speed Chaos Search operator
Major part document carries out Chaos Search with logistic mappings at present, but is had shown that by research
Its distribution of the produced Chaos Variable of logistic mappings is simultaneously non-homogeneous, haves the shortcomings that border Distribution value is more.And kent
Chaos Variable produced by mapping is evenly distributed, it is adaptable to the need for this method, therefore this method takes kent mappings to be mixed
Ignorant search, its iterative formula such as formula (13).
Step (1)：The speed vgb of history adaptive optimal control degree particle is mapped in the interval of (0,1), mapping equation such as formula
(14)。
Step (2)：Judge whether the speed vgb of history adaptive optimal control degree particle is updated, the hdjs=0 if being updated,
Otherwise hdjs=hdjs+1.
Step (3)：The speed vgb of history adaptive optimal control degree particle after normalizingb' (b=1,2,56) it is brought into
Kent mappings produce chaos sequence zmb(m=1,2,20hdjs+20), kent maps such as formula (13), in the method,
φ values are 0.3.
Step (4)：By 20 z after chaos sequencemb(m=20hdjs+1,20hdjs+2,20hdjs+20) carrier wave
Into former solution space, formula such as formula (15).
v′mb=vmin+(vmax-vmin)zmb (15)
Step (5)：The new explanation produced is mapped according to kent and former solution carries out inferior position particle u speed b renewal, such as formula
(16), then operator terminates.
vub=λ vub+(1-λ)v′mb (16)
Wherein,
Step 3.8：All particle i position j, wherein g (v is updated according to (5) formulaij) function such as formula (17).
If vij＞ vmax, then vij=vmax.If vij＜ vmin, then vij=vmin。
Step 3.9：Statistics particle i middle positions are set to 1 number, if equal to rn goes to step 3.10, otherwise using reparation
Restricted operator enters row constraint to the position of particle.
Repair Restricted operator
With being continuously increased for iterations, to make inferior position particle travel through solution space.And repair number rn's to meet
It is required that so that all particles be feasible solution to improve the efficiency of algorithm, that is, take following steps.If particle i middle positions are set to 1
Number sum gs (i) is more than rn, then goes to step (1), otherwise go to step (2).
Step (1)：Step (a) is gone to if particle is advantage particle；If particle be ordinary particle andThen go to step (a).Otherwise, step (b) is gone to；If particle is inferior position particle, step is gone to
(b)。
Step (a):Make value in particle i be changed into 0 at random for 1 position, if in particle i value for 1 position number it
It is equal to rn with gs (i), then operator is terminated, and goes to step 3.10, otherwise repeat step (a).
Step (b):To increase the diversity of population so that 1 more position of number occur in population and be changed into 0, make out
Existing 1 less position of number is preserved, to increase the possibility for jumping out local maximum.Take following steps：
1. the number of times og (j) that all position j are 1 in population is calculated.
2. by the number of times normalizing of position appearance 1 in population to [- 1,1].Then the data os (j) after position j normalizings is calculated such as
Formula (18).
Wherein ogmin, ogmaxThere is the minimum value and maximum of 1 number for all particle positions in population.
3. j=0, js=0 are made.
4. j=j+1, calculates op (j) such as formula (19).
Op (j)=F (os (j)) (19)
Wherein
If 5. rand ＜ op (j) and p (i, j)=1, then p (i, j)=0, js=js+1.
If 6. j=n, j=0.
If 7. js=gs (i)-rn, terminates to repair Restricted operator and goes to step 3.10, otherwise go to 4..
Step (2)：Step (a) is gone to if particle is advantage particle；If particle be ordinary particle andThen go to step (a).Otherwise, step (b) is gone to；If particle is inferior position particle, step is gone to
(b)。
Step (a):Make value in particle i be changed into 1 at random for 0 position, if in particle i value for 1 position number it
With equal to rn, then operator termination, goes to step 3.10, otherwise repeat step (a).
Step (b):
1. the number of times og (j) that all position j are 1 in population is calculated.
2. by the number of times normalizing of position appearance 1 in population to [- 1,1].Then the data os (j) after position j normalizings is calculated such as
Formula (18).
3. j=0, js=0 are made.
4. j=j+1, calculates op (j) such as formula (19).
If 5. rand ＞ op (j) and p (i, j)=0, then p (i, j)=1, js=js+1.
If 6. j=n, j=0.
If 7. js=rn-gs (i), terminates to repair Restricted operator and goes to step 3.10, otherwise go to 4..
Step 3.10：Calculate each particle i fitness f (i), calculating process such as step 3.3.
Step 3.11：To ranking fitness, 20% particle is advantage particle, selection 20% before fitness in selection particle
The particle of individual fitness rearward is inferior position particle, and remaining is then ordinary particle.
Step 3.12：If f (i) ＞ fib (i), by position of particle i position assignment when particle i adaptive optimal controls are spent,
More new particle i adaptive optimal control degree.If f (i) ＞ fgb, by particle i position assignment in all particle history adaptive optimal control degree
When position, update the history adaptive optimal control degree of all particles and the speed vgb of history adaptive optimal control degree in population.
Step 3.13：Iterations t is updated, judges whether t ＞ 200, step 3.5 is turned to if not meeting, if meeting
Go to step 3.14.The history adaptive optimal control degree of each iteration population is as shown in Figure 8.
Step 3.14：History adaptive optimal control degree in population and its position are exported.When then history adaptive optimal control is spent in population
Position, you can correspond to group of cities transportation network cascading failure preferably recovery scenario, repair the change of deutomerite dotted state such as
Shown in table 4, population history adaptive optimal control degree position value is as shown in table 5.
Using bus station as the node of Traffic Net in this method, using railway station as the node of Rail traffic network, with
Airport is the node of air transportation network, using harbour as the node of water-borne transport network.Other schemes may be using city as network
In node, can also build group of cities traffic network design；This method constructs city based on a variety of traffic network designs
Group's traffic network design, other schemes may then build single traffic network design.This method is tactful to handing over what is attacked at random
Open network is attacked, other schemes can also with calculated attack, equally can be with based on betweenness attack or other attack patterns
So that node failure, in step 3, this method are repaiied using binary particle swarm algorithm is improved to group of cities transportation network reliability
Compound case is optimized.Alternate embodiments can also complete identical purpose, such as binary system heredity using other optimized algorithms
Algorithm, simulated annealing, binary ant colony algorithm, immunity particle cluster algorithm etc..
Three kinds of states of the invention according to node, it is contemplated that cascading failure phenomenon present in transportation network, can be imitative
Very, the influence between egress and node is embodied in repairing.According in network while importance for while impart weight, Neng Gouzhun
True measurement group of cities transportation network reliability is by being influenceed.Consider load with the characteristic for repairing node state change, i.e., it is every
The process of pause node load can be shared by repairing normal node in a failure node, network, can more objectively be described
Group of cities traffic flow phenomenon.Improve binary particle swarm algorithm, it is proposed that fine disturbing operator and speed Chaos Search are calculated
Son, is coordinated by advantage particle and inferior position particle cooperative and on the one hand improves the fine degree understood, on the other hand add particle
In the search capability of solution space.In addition repairing Restricted operator causes all particles to be feasible solution to ensure efficient, the letter of algorithm
Just, and it has been used in during group of cities transportation network repairs, using the teaching of the invention it is possible to provide preferably recovery scenario, has farthest recovered city
The reliability of city's flock-mate open network.
Table 1. attacks the state of posterior nodal point
The change of network reliability after table 2. is attacked
The particle position sequence number of table 3. and node ID corresponding relation
Table 4. repairs the state of posterior nodal point
The value of the population history adaptive optimal control degree position of table 5.
The preferred embodiments of the present invention are the foregoing is only, are not intended to limit the scope of the invention, it is every to utilize
Equivalent structure or equivalent flow conversion that description of the invention and accompanying drawing content are made, or directly or indirectly it is used in other correlations
Technical field, be included within the scope of the present invention.
Claims (4)
1. the group of cities transportation network reliability restorative procedure under random attack strategies, it is characterised in that：Its method and step is：Step
Rapid 1 is structure group of cities traffic network design；Step 2 emulates for group of cities transportation network cascading failure；Step 3 is based on improvement
The group of cities transportation network reliability restorative procedure of binary particle swarm algorithm, the step 1 also includes：
Step 1.1：The classification existed according to group of cities transportation network, builds in single traffic network design, such as group of cities and exists
Four kinds of means of transportation, then need to build respectively Traffic Net model, Rail traffic network model, air transportation network model,
Water-borne transport network model；
Step 1.2：In various traffic network designs, if bus station, railway station, airport, harbour geographical position it is nearer, it is right
Node is overlapped, and a node is regarded it as in group of cities transportation network；
Step 1.3：With the departure frequency of automobile, train start train number, the flight frequency of aircraft, ship course line order of classes or grades at school point
Not as the weight on side in Traffic Net, Rail traffic network, air transportation network, water-borne transport network, with entropy weight
Method tries to achieve the significance level of every kind of means of transportation, and finally side ij weight ew (i, j) is important journey in group of cities transportation network
The product of degree and side right weight in single transportation network；
Step 1.4：Gather number according to bus station, railway station, airport, passenger's highest at harbour, determine nodes i appearance
C (i) is measured, then the node capacity after being superimposed is superposition front nodal point capacity sum.
2. the group of cities transportation network reliability restorative procedure under random attack strategies according to claim 1, its feature
It is：Step 1.1 further comprises：
Step 1.1.1：Using the bus station in group of cities as the node in Traffic Net, if being open to traffic between bus station, save
There is a line between point to be connected, Traffic Net model is built with this；
Step 1.1.2：Using the railway station in group of cities as the node in Rail traffic network, if there is track circuit between railway station
It is connected, then there is a line between node and be connected, Rail traffic network model is built with this；
Step 1.1.3：Node in using the airport in group of cities as air transportation network, if there is schedule flight between airport,
There is a line between node to be connected, air transportation network model is built with this；
Step 1.1.4：Node in using the harbour in group of cities as water-borne transport network, if there is navigation ship between harbour,
Then there is a line between node to be connected, water-borne transport network model is built with this.
3. the group of cities transportation network reliability restorative procedure under random attack strategies according to claim 1, its feature
It is：Step 2 further comprises：
Step 2.1：According to capacity coefficient α, it may be determined that node i is not attacking load l (i) such as formulas (1) at moment；
L (i)=α * c (i) (1)
Step 2.2：With the strategy attack node i attacked at random；
Step 2.3：Node i fail, judge whether normal condition and connected node j, if in the presence of if load l (i) distribute
To coupled node j, node j load such as formula (2) goes to step 2.5 if being not present；
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Wherein, d (j) is node j node degree, the i.e. connected side number of node, and Φ is the set being connected with node i；
Step 2.4：Judge connected node j state；
Wherein, β is overload factor.If node failure, step 2.3 is gone to, step 2.5 is otherwise gone to；
Step 2.5：Judge that pause node whether there is the normal connected node of state, if there is then carrying out sharing of load；
Step 2.6：Judge whether to travel through all pause nodes, if then judging all node states according to formula (3), and go to step
Rapid 2.7, otherwise go to step 2.5；
Step 2.7：Iterations is updated, and judges whether iterations is less than number of times of attack, such as iterations is less than attack time
Number, then return to step 2.2, otherwise terminate cascading failure emulation.
4. the group of cities transportation network reliability restorative procedure under random attack strategies according to claim 1, its feature
It is：Step 3 further comprises：
Step 3.1：If if there is dried particle in population, each particle is then a kind of recovery scenario, and the dimension all same of particle is lost
Nodes n is imitated, speed and position are initialized, and calculate the fitness of each particle；
Step 3.2：Advantage particle, ordinary particle and inferior position grain are selected from the population of initialization according to ranking fitness
Son；
Step 3.3：The position of each particle corresponds to a speed, then the speed of j-th of dimension in particle i is vij, update
Speed such as formula (4)；
vij=w*vij+rand*c1*(pibij-pij)+rand*c2*(pgbj-pij) (4)
Wherein, w is inertia weight, and rand is 0 to 1 random number, c1,c2Respectively the self-teaching factor and social learning's factor,
pibijFor the value of i-th of particle adaptive optimal control j-th of dimension of degree, pgbjTieed up for j-th for all particle history adaptive optimal control degree
The value of degree；
Step 3.4：The speed of advantage particle is disturbed with fine disturbing operator；
Step 3.5：The speed of inferior position particle is updated with speed Chaos Search operator；
Step 3.6：According to the speed of particle, then particle i positions j renewal public affairs are such as formula (5)；
Step 3.7：Row constraint is entered to the position of each particle with Restricted operator is repaired；
Step 3.8：Each particle i fitness f (i) is calculated, if f (i) ＞ fib (i), by particle i position assignment in grain
The adaptive optimal control degree of position when sub- i adaptive optimal controls are spent, more new particle i, if f (i) ＞ fgb, by particle i position assignment in
Position when history adaptive optimal control is spent in all particles, updates all particle history adaptive optimal control degree and speed, wherein, fib (i)
For the fitness that particle i is optimal, fgb is the optimal fitness of all particle history；
Step 3.9：To ranking fitness, advantage particle, ordinary particle and inferior position particle are selected；
Step 3.10：Iterations is updated, judges whether to have reached greatest iteration number, step 3.3 is turned to if not meeting, if full
Sufficient then export history adaptive optimal control degree in population and its position, then its position value is that group of cities transportation network is preferably repaired
Scheme.
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